Question: Simplify the following expression: $ p = \dfrac{-2}{5} - \dfrac{z + 5}{9z + 2} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9z + 2}{9z + 2}$ $ \dfrac{-2}{5} \times \dfrac{9z + 2}{9z + 2} = \dfrac{-18z - 4}{45z + 10} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{z + 5}{9z + 2} \times \dfrac{5}{5} = \dfrac{5z + 25}{45z + 10} $ Therefore $ p = \dfrac{-18z - 4}{45z + 10} - \dfrac{5z + 25}{45z + 10} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-18z - 4 - (5z + 25) }{45z + 10} $ Distribute the negative sign: $p = \dfrac{-18z - 4 - 5z - 25}{45z + 10}$ $p = \dfrac{-23z - 29}{45z + 10}$